↑

Properties

Label 40T1730
Degree $40$
Order $2000$
Cyclic no
Abelian no
Solvable yes
Primitive no
$p$-group no
Group: $C_{10}\times D_5\wr C_2$

Related objects

Downloads

Learn more

Show commands: Magma

Copy content magma:G := TransitiveGroup(40, 1730);
 

Group invariants

Abstract group:  $C_{10}\times D_5\wr C_2$
Copy content magma:IdentifyGroup(G);
 
Order:  $2000=2^{4} \cdot 5^{3}$
Copy content magma:Order(G);
 
Cyclic:  no
Copy content magma:IsCyclic(G);
 
Abelian:  no
Copy content magma:IsAbelian(G);
 
Solvable:  yes
Copy content magma:IsSolvable(G);
 
Nilpotency class:   not nilpotent
Copy content magma:NilpotencyClass(G);
 

Group action invariants

Degree $n$:  $40$
Copy content magma:t, n := TransitiveGroupIdentification(G); n;
 
Transitive number $t$:  $1730$
Copy content magma:t, n := TransitiveGroupIdentification(G); t;
 
Parity:  $1$
Copy content magma:IsEven(G);
 
Primitive:  no
Copy content magma:IsPrimitive(G);
 
$\card{\Aut(F/K)}$:  $10$
Copy content magma:Order(Centralizer(SymmetricGroup(n), G));
 
Generators:  $(1,17,7,11,3,15,9,20,5,14)(2,18,8,12,4,16,10,19,6,13)(21,40)(22,39)(23,32)(24,31)(25,34)(26,33)(27,35)(28,36)(29,37)(30,38)$, $(1,36,7,32,3,38,9,33,5,40)(2,35,8,31,4,37,10,34,6,39)(11,30,20,21,17,23,15,26,14,28)(12,29,19,22,18,24,16,25,13,27)$, $(1,19,27,36,3,18,29,38,5,16,22,40,7,13,24,32,9,12,25,33)(2,20,28,35,4,17,30,37,6,15,21,39,8,14,23,31,10,11,26,34)$
Copy content magma:Generators(G);
 

Low degree resolvents

$\card{(G/N)}$Galois groups for stem field(s)
$2$:  $C_2$ x 7
$4$:  $C_2^2$ x 7
$5$:  $C_5$
$8$:  $D_{4}$ x 2, $C_2^3$
$10$:  $C_{10}$ x 7
$16$:  $D_4\times C_2$
$20$:  20T3 x 7
$40$:  20T12 x 2, 40T7
$80$:  40T20
$200$:  $D_5^2 : C_2$
$400$:  20T92
$1000$:  $D_5^2:C_{10}$

Resolvents shown for degrees $\leq 47$

Subfields

Degree 2: $C_2$ x 3

Degree 4: $C_2^2$, $D_{4}$ x 2

Degree 5: None

Degree 8: $D_4\times C_2$

Degree 10: None

Degree 20: $D_5^2:C_{10}$

Low degree siblings

40T1730 x 7

Siblings are shown with degree $\leq 47$

A number field with this Galois group has no arithmetically equivalent fields.

Conjugacy classes

Conjugacy classes not computed

Copy content magma:ConjugacyClasses(G);
 

Character table

140 x 140 character table

Copy content magma:CharacterTable(G);
 

Regular extensions

Data not computed